General Equation of Circle S=0

Q.

Write the coordinates of the centre of the circle passing through (0, 0), (4, 0) and (0, -6).

Q.

A circle of radius ‘5’ touches the coordinate axes in the first quadrant. If the circle makes one complete roll on x-axis along the positive direction, then its equation in new position is

1. 

2. 

3. 

4. 

Q.

The circle $x^2+y^2+2gx+2fy+c=0$ does not intersect x-axis, if

1. $g^2<c$
   

2. $g^2>c$
   

3. $g^2>2c$

4. none of these

Q. Find the area of the region enclosed between the two circles $x^2+y^2=4$ and $(x-2)+y^2=4$.

Q.

Find the equation of the circle whose diameter is the line segment joining (-4, 3) and (12, -1). Find also the intercept made by it on y-axis.

Q.

Find the equations of the circles which pass through the origin and cut off equal chords of $\sqrt{2}$ units from the lines y = x and y = -x.

Q. The equation of the image of the circle $x^2+y^2+16x–24y+183=0$ by the line mirror 4x + 7y + 13 = 0

1. 
2. 
3. 
4. 

Q.

Write the equation of the circle passing through (3, 4) and touching y-axis at the origin.

Q. $P$ is a point on $y^2=4ax(a>0)$ whose vertex is $A$. $PA$ is produced to meet the directrix in $D$ and $M$ is the foot of perpendicular from $P$ on the directrix. If a circle is described on $MD$ as a diameter then it intersects $x-$axis at

1. $(–3a,0)$
2. $(–2a,0)$
3. $(a,0)$
4. $(–a,0)$

Q.

Which of the following is/are the equation of a circle?

1. 

2. 

3. 

4. 

Q. The equation of a circle which touches both axes and the line 3x – 4y + 8 = 0 and whose centre lies in the third quadrant is

1. 
2. 
3. 
4. 

Q. A line passing through $P(1,2)$ inclined at an angle $\theta$ with positive $x-$axis cuts the circle $x^2+y^2-6x-8y+24=0$ at $A$ and $B$ such that $PA+PB=4\sqrt{2}.$ Then the value of $\cos \theta +\sin \theta$ is

1. $\sqrt{2}$
2. $2\sqrt{2}$
3. $\frac{1}{2\sqrt{2}}$
4. $\frac{1}{\sqrt{2}}$

Q. If the circle $x^2+y^2+2x+4y-p=0$ and the coordinate axes have exactly three common points, then p =

1. 1
2. -1
3. 2
4. -4

Q.

The equation of a circle with radius 5 and touching both die coordinate axes is

1. $x^2+y^2\pm 10x\pm 10y=0$

2. $x^2+y^2\pm 10x\pm 10y+25=0$

3. $x^2+y^2\pm 10x\pm 10y+51=0$

4. $x^2+y^2\pm 10x\pm 10y+5=0$

Q. If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is

1. (b, a)
2. $(\frac{a}{2},\frac{b}{2})$
3. (a, b)
4. $(\frac{b}{2},\frac{a}{2}).$

Q. The line $x=\sqrt{3}y$ intersects with the curve $y^3-x^2-3y^2+8=0$ at the points $A,B$ and $C$. If $O$ be the origin, then $|OA.OB.OC|$ equals

1. $72$
2. $64$
3. $8$
4. $\frac{8}{\sqrt{3}}$

Q. The equation of the image of the circle $x^2+y^2$ - 6x - 4y + 12 = 0 by the line mirror x + y - 1 = 0

1. $x^2+y^2$ + 2x + 4y + 4 = 0
2. $x^2+y^2$ - 2x + 4y + 4 = 0
3. $x^2+y^2$ + 2x + 4y - 4 = 0
4. $x^2+y^2$ + 2x - 4y - 4 = 0

Q. From the point A(0, 3) on the circle $x^2+4x+(y–3{)}^2=0$ a chord AB is drawn and extended to a point M such that AM = 2 AB. The equation of the locus of M is

1. 
2. 
3. 
4. 

Q.

If $(m_i,\frac{1}{m_i})$, i = 1, 2, 3, 4 are con - cyclic points, then the value of $m_1{m}_2{m}_3{m}_4$ is

1. 1

2. -1

3. 0

4. 2

Q. From the point A (0, 3) on the circle $x^2+4x+(y-3{)}^2=0$ a chord AB is drawn and extended to a point M such that AM =2AB. The equation of the locus of M is___

1. $x^2+y^2+6x-8y+9=0$
2. $x^2+y^2-6x+8y+9=0$
3. $x^2+y^2-8x+6y+9=0$
4. $x^2+y^2+8x-6y+9=0$

Q.

$(2+2\lambda +\mu )x^2+(1+2\lambda +2\mu )y^2+(3+5\lambda +3\mu )xy$

$-(16+14\lambda +11\mu )x-(10+13\lambda +17\mu )+(24+20\lambda +30\mu )=0$ is an equation of circle only when

1. $\lambda =1\mu =1$

2. $\lambda =-2\mu =\frac{-12}{11}$

3. $\lambda =1\mu =0$

4. $\lambda =\frac{-6}{5}\mu =1$

Q.

If $(m_i,\frac{1}{m_i})$, i = 1, 2, 3, 4 are con - cyclic points, then the value of $m_1{m}_2{m}_3{m}_4$ is

1. 1

2. -1

3. 0

4. 2

Q. If $\lambda x^2+\mu y^2+(\lambda \mu -4)xy-\lambda x-\mu y-20=0$ represents a circle, the radius of the circle is

1. $\sqrt{\frac{21}{2}}$
2. $2\sqrt{21}$
3. $\sqrt{\frac{42}{2}}$
4. $\sqrt{}22$

Q. The equation $a{x}^2+b{y}^2+2hxy+2gx+2fy+c=0$ will represent a circle, if

1. a = b = 0 and c = 0
2. f = g and h = 0
3. and h = 0
4. f = g and c = 0

Q. If the equation $\frac{K(x+1{)}^2}{3}+\frac{(y+2{)}^2}{4}=1$ represents a circle, then K =

1. 3/4
2. 1
3. 4/3
4. 12

Q. If the equation $\frac{K(x+1{)}^2}{3}+\frac{(y+2{)}^2}{4}=1$ represents a circle, then K =

1. 3/4
2. 1
3. 4/3
4. 12

Q. For how many values of $p$, the circle $x^2+y^2+2x+4y-p=0$ and the coordinate axes have exactly three common points? .
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Q.

Find the area bounded by curves $\left\{\right(x,y):y\ge x^{2}andy\le |x|$

Q. If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is

1. (a, b)
2. (b, a)
3. $(\frac{a}{2},\frac{b}{2})$
4. $(\frac{b}{2},\frac{a}{2}).$

Q. Find the equation of the circle are which passes through the point ( 1 , -2) and (3, -4) and touched the axis of x